The Lyapunov order for real matrices

Nir Cohen, Izchak Lewkowicz

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The real Lyapunov order in the set of real n × n matrices is a relation defined as follows: A ≤ B if, for every real symmetric matrix S, SB + Bt S is positive semidefinite whenever SA + At S is positive semidefinite. We describe the main properties of the Lyapunov order in terms of linear systems theory, Nevenlinna-Pick interpolation and convexity.

Original languageEnglish
Pages (from-to)1849-1866
Number of pages18
JournalLinear Algebra and Its Applications
Issue number7
StatePublished - 1 Apr 2009


  • Controllability
  • Convex cone
  • Convex invertible cone
  • Lyapunov matrix equation
  • Pick matrix

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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